arXiv subjects

Akshay Gaikwad

Publications and source records attributed to Akshay Gaikwad.

17 recordsLinked to original sources

arXiv2026

Heuristically optimizing, synthesizing, and prioritizing measurement settings for quantum state tomography

A key task in many quantum-computing applications, e.g., quantum simulation and quantum state tomography (QST), is to partition an arbitrary set of operators into mutually commuting subsets for efficient measurements. However, brute-force approaches to this task quickly become intractable as the number and dimensionality of operators grow. Here, we reformulate operator partitioning as a graph-coloring (GC) problem and develop an efficient computational framework to solve it, balancing accuracy and efficiency. Our framework enables leveraging a range of GC algorithms, which we benchmark for operator partitioning. Then, we demonstrate their utility in optimizing QST experiments, where determining non-overlapping data acquisition settings for QST is a major challenge, and prioritizing among these settings, i.e., selecting the experiments that provide the most information. We further show how to perform these experiments by synthesizing Clifford circuits for joint measurement of commuting Pauli operators in multi-qubit systems. We validate our framework across multi-qubit (up to five qubits), multi-qutrit (up to three qutrits), and hybrid qubit-qutrit systems. Our results show that heuristic GC methods substantially reduce the number of required measurement settings for QST and enable priority-based scheduling that maximizes the information gain per experiment. The optimization converges within minutes on a student-grade laptop, providing speedups of several orders of magnitude over brute-force methods already for these relatively small quantum systems. This demonstrates the potential of GC heuristics as a scalable and practical tool for characterization of noisy intermediate-scale quantum devices. We have made the Python implementation of our GC framework to optimize and schedule QST experiments publicly available at https://github.com/ssm8015/QST_GT.git.

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arXiv2025

Quantum measurement tomography with mini-batch stochastic gradient descent

Drawing inspiration from gradient-descent methods developed for data processing in quantum state tomography [\href{https://iopscience.iop.org/article/10.1088/2058-9565/ae0baa}{Quantum Sci.~Technol.~\textbf{10} 045055 (2025)}] and quantum process tomography [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.150402}{Phys.~Rev.~Lett.~\textbf{130}, 150402 (2023)}], we introduce stochastic gradient descent (SGD) algorithms for fast quantum measurement tomography (QMT), applicable to both discrete- and continuous-variable quantum systems -- thus completing the tomography trio. A measurement device or detector in a quantum experiment is characterized by a set of positive operator-valued measure (POVM) elements; the goal of QMT is to estimate these operators from experimental data. To ensure physically valid (positive and complete) POVM reconstructions, we propose two distinct parameterization schemes within the SGD framework: one leveraging optimization on a Stiefel manifold and one based on Hermitian operator normalization via eigenvalue scaling. Within the SGD-QMT framework, we further investigate two loss functions: mean squared error, equivalent to L2 or Euclidean norm, and average negative log-likelihood, inspired by maximum likelihood estimation. We benchmark performance against state-of-the-art constrained convex optimization methods. Numerical simulations demonstrate that, compared to standard methods, our SGD-QMT algorithms offer significantly lower computational cost, superior reconstruction fidelity, and enhanced robustness to noise. We make a Python implementation of the SGD-QMT algorithms publicly available at \href{https://github.com/agtomo/SGD-QMT}{github.com/agtomo/SGD-QMT}.

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arXiv2025

Quantum Process Tomography with Digital Twins of Error Matrices

Accurate and robust quantum process tomography (QPT) is crucial for verifying quantum gates and diagnosing implementation faults in experiments aimed at building universal quantum computers. However, the reliability of QPT protocols is often compromised by faulty probes, particularly state preparation and measurement (SPAM) errors, which introduce fundamental inconsistencies in traditional QPT algorithms. We propose and investigate enhanced QPT for multi-qubit systems by integrating the error matrix in a digital twin of the identity process matrix, enabling statistical refinement of SPAM error learning and improving QPT precision. Through numerical simulations, we demonstrate that our approach enables highly accurate and faithful process characterization. We further validate our method experimentally using superconducting quantum gates, achieving at least an order-of-magnitude fidelity improvement over standard QPT. Our results provide a practical and precise method for assessing quantum gate fidelity and enhancing QPT on a given hardware.

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arXiv2025

Selective and efficient quantum state tomography for multi-qubit systems

Quantum state tomography (QST) is a crucial tool for characterizing quantum states. However, QST becomes impractical for reconstructing multi-qubit density matrices since data sets and computational costs grow exponentially with qubit number. In this Letter, we introduce selective and efficient QST (SEEQST), an approach for efficiently estimating multiple selected elements of an arbitrary $N$-qubit density matrix. We show that any $N$-qubit density matrix can be partitioned into $2^N$ subsets, each containing $2^N$ elements. With SEEQST, any such subset can be accurately estimated from just two experiments with only single-qubit measurements. The complexity for estimating any subset remains constant regardless of Hilbert-space dimension, so SEEQST can find the full density matrix using $2^{N+1} - 1$ experiments, where standard methods would use $3^N$ experiments. We provide a circuit decomposition for the SEEQST experiments, demonstrating that their maximum circuit depth scales logarithmically with $N$ assuming all-to-all connectivity. The Python code for SEEQST is publicly available at \href{https://github.com/aniket-ae/SEEQST}{github.com/aniket-ae/SEEQST}.

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arXiv2025

Gradient-descent methods for fast quantum state tomography

Quantum state tomography (QST) is a widely employed technique for characterizing the state of a quantum system. However, it is plagued by two fundamental challenges: computational and experimental complexity grows exponentially with the number of qubits, rendering experimental implementation and data post-processing arduous even for moderately sized systems. Here, we introduce gradient-descent (GD) algorithms for the post-processing step of QST in discrete- and continuous-variable systems. To ensure physically valid state reconstruction at each iteration step of the algorithm, we use various density-matrix parameterizations: Cholesky decomposition, Stiefel manifold, and projective normalization. These parameterizations have the added benefit of enabling a rank-controlled ansatz, which simplifies reconstruction when there is prior information about the system. We benchmark the performance of our GD-QST techniques against state-of-the-art methods, including constrained convex optimization, conditional generative adversarial networks, and iterative maximum likelihood estimation. Our comparison focuses on time complexity, iteration counts, data requirements, state rank, and robustness against noise. We find that rank-controlled ansatzes in our stochastic mini-batch GD-QST algorithms effectively handle noisy and incomplete data sets, yielding significantly higher reconstruction fidelity than other methods. Simulations achieving full-rank seven-qubit QST in under three minutes on a standard laptop, with 18 GB of RAM and no dedicated GPU, highlight that GD-QST is computationally more efficient and outperforms other techniques in most scenarios, offering a promising avenue for characterizing noisy intermediate-scale quantum devices. Our Python code for GD-QST algorithms is publicly available at https://github.com/mstorresh/GD-QST.

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arXiv2024

Quantum SWAP gate realized with CZ and iSWAP gates in a superconducting architecture

It is advantageous for any quantum processor to support different classes of two-qubit quantum logic gates when compiling quantum circuits, a property that is typically not seen with existing platforms. In particular, access to a gate set that includes support for the CZ-type, the iSWAP-type, and the SWAP-type families of gates, renders conversions between these gate families unnecessary during compilation as any two-qubit Clifford gate can be executed using at most one two-qubit gate from this set, plus additional single-qubit gates. We experimentally demonstrate that a SWAP gate can be decomposed into one iSWAP gate followed by one CZ gate, affirming a more efficient compilation strategy over the conventional approach that relies on three iSWAP or three CZ gates to replace a SWAP gate. Our implementation makes use of a superconducting quantum processor design based on fixed-frequency transmon qubits coupled together by a parametrically modulated tunable transmon coupler, extending this platform's native gate set so that any two-qubit Clifford unitary matrix can be realized using no more than two two-qubit gates and single-qubit gates.

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arXiv2024

Deterministic generation of frequency-bin-encoded microwave photons

A distributed quantum computing network requires a quantum communication channel between spatially separated processing units. In superconducting circuits, such a channel can be implemented based on propagating microwave photons to encode and transfer quantum information between an emitter and a receiver. However, traveling microwave photons can be lost during the transmission, leading to the failure of information transfer. Heralding protocols can be used to detect such photon losses. In this work, we propose such a protocol and experimentally demonstrate a frequency-bin encoding method of microwave photonic modes using superconducting circuits. We deterministically encode the quantum information from a superconducting qubit by simultaneously emitting its information into two photonic modes at different frequencies, with a process fidelity of 90.4%. The frequency-bin-encoded photonic modes can be used, at the receiver processor, to detect the occurrence of photon loss. Our work thus provides a reliable method to implement high-fidelity quantum state transfer in a distributed quantum computing network, incorporating error detection to enhance performance and accuracy.

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arXiv2024

Experimental decoherence mitigation using a weak measurement-based scheme and the duality quantum algorithm

We experimentally demonstrate a weak measurement and measurement reversal-based scheme to ameliorate the effects of decoherence due to amplitude damping, on an NMR quantum processor. The weak measurement and measurement reversal processes require the implementation of non-unitary operations, which are typically infeasible on conventional quantum processors, where only unitary quantum operations are allowed. The duality quantum algorithm is used to efficiently implement the required non-unitary quantum operations corresponding to weak measurement and measurement reversal. We experimentally validate the efficacy of the weak measurement-based decoherence mitigation scheme by showing state protection on a four-qubit system, with one qubit being designated as the 'system qubit', while the remaining three qubits serve as 'ancilla qubits'. Our experimental results clearly demonstrate the success of the weak measurement-based decoherence mitigation scheme in protecting the desired state. Since the measurement process involved has trace less than unity, the scheme can be thought of as a filtration scheme, where a subset of the spins is protected while the rest of the spins can be discarded.

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arXiv2024

Entanglement of photonic modes from a continuously driven two-level system

The ability to generate entangled states of light is a key primitive for quantum communication and distributed quantum computation. Continuously driven sources, including those based on spontaneous parametric downconversion, are usually probabilistic, whereas deterministic sources require accurate timing of the control fields. Here, we experimentally generate entangled photonic modes by continuously exciting a quantum emitter, a superconducting qubit, with a coherent drive, taking advantage of mode matching in the time and frequency domain. Using joint quantum state tomography and logarithmic negativity, we show that entanglement is generated between modes extracted from the two sidebands of the resonance fluorescence spectrum. Because the entangled photonic modes are perfectly orthogonal, they can be transferred into distinct quantum memories. Our approach can be utilized to distribute entanglement at a high rate in various physical platforms, with applications in waveguide quantum electrodynamics, distributed quantum computing, and quantum networks.

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arXiv2024

Novel techniques for efficient quantum state tomography and quantum process tomography and their experimental implementation

This thesis actively focuses on designing, analyzing, and experimentally implementing various QST and QPT protocols using an NMR ensemble quantum processor and superconducting qubit-based IBM cloud quantum processor. Part of the thesis also includes a study of duality quantum simulation algorithms and Sz-Nagy's dilation algorithm on NMR where several 2-qubit non-unitary quantum channels were simulated using only a single ancilla qubit. The work carried out in the thesis mainly addresses several important issues in experimental QST and QPT which include: i) dealing with invalid experimental density (process) matrices using constraint convex optimization (CCO) method, ii) scalable QST and QPT using incomplete measurements via compressed sensing (CS) algorithm and artificial neural network (ANN) technique, iii) selective and direct measurement of unknown quantum states and processes using the concept of quantum 2-design states and weak measurement (WM) approach and iv) quantum simulation and characterization of open quantum dynamics using the dilation technique.

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arXiv2023

Neural network assisted quantum state and process tomography using limited data sets

In this study we employ a feed-forward artificial neural network (FFNN) architecture to perform tomography of quantum states and processes obtained from noisy experimental data. To evaluate the performance of the FFNN, we use a heavily reduced data set and show that the density and process matrices of unknown quantum states and processes can be reconstructed with high fidelity. We use the FFNN model to tomograph 100 two-qubit and 128 three-qubit states which were experimentally generated on a nuclear magnetic resonance (NMR) quantum processor. The FFNN model is further used to characterize different quantum processes including two-qubit entangling gates, a shaped pulsed field gradient, intrinsic decoherence processes present in an NMR system, and various two-qubit noise channels (correlated bit flip, correlated phase flip and a combined bit and phase flip). The results obtained via the FFNN model are compared with standard quantum state and process tomography methods and the computed fidelities demonstrates that for all cases, the FFNN model outperforms the standard methods for tomography.

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arXiv2023

Direct tomography of quantum states and processes via weak measurements of Pauli spin operators on an NMR quantum processor

In this paper, we present an efficient weak measurement-based scheme for direct quantum state tomography (DQST) and direct quantum process tomography (DQPT), and experimentally implement it on an NMR ensemble quantum information processor without involving any projective measurements. We develop a generalized quantum circuit that enables us to directly measure selected elements of the density matrix and process matrix which characterize unknown quantum states and processes, respectively. This generalized quantum circuit uses the scalar J-coupling to control the interaction strength between the system qubits and the metre qubit. We experimentally implement these weak measurement-based DQST and DQPT protocols and use them to accurately characterize several two-qubit quantum states and single-qubit quantum processes. An extra qubit is used as a metre qubit to implement the DQST protocol, while for the DQPT protocol, two extra qubits (one as a metre qubit and the other as an ancilla qubit) are used.

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arXiv2022

Simulating open quantum dynamics on an NMR quantum processor using the Sz.-Nagy dilation algorithm

We experimentally implement the Sz.-Nagy dilation algorithm to simulate open quantum dynamics on an nuclear magnetic resonance (NMR) quantum processor. The Sz.-Nagy algorithm enables the simulation of the dynamics of arbitrary-dimensional open quantum systems, using only a single ancilla qubit. We experimentally simulate the action of two non-unitary processes, namely, a phase damping channel acting independently on two qubits and a magnetic field gradient pulse (MFGP) acting on an ensemble of two coupled nuclear spin-1/2 particles. To evaluate the quality of the experimentally simulated quantum process, we perform convex optimization-based full quantum process tomography to reconstruct the quantum process from the experimental data and compare it with the target quantum process to be simulated.

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arXiv2021

Efficient experimental characterization of quantum processes via compressed sensing on an NMR quantum processor

We employ the compressed sensing (CS) algorithm and a heavily reduced data set to experimentally perform true quantum process tomography (QPT) on an NMR quantum processor. We obtain the estimate of the process matrix $\chi$ corresponding to various two- and three-qubit quantum gates with a high fidelity. The CS algorithm is implemented using two different operator bases, namely, the standard Pauli basis and the Pauli-error basis. We experimentally demonstrate that the performance of the CS algorithm is significantly better in the Pauli-error basis, where the constructed $\chi$ matrix is maximally sparse. We compare the standard least square (LS) optimization QPT method with the CS-QPT method and observe that, provided an appropriate basis is chosen, the CS-QPT method performs significantly better as compared to the LS-QPT method. In all the cases considered, we obtained experimental fidelities greater than 0.9 from a reduced data set, which was approximately five to six times smaller in size than a full data set. We also experimentally characterized the reduced dynamics of a two-qubit subsystem embedded in a three-qubit system, and used the CS-QPT method to characterize processes corresponding to the evolution of two-qubit states under various $J$-coupling interactions.

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arXiv2021

Implementing efficient selective quantum process tomography of superconducting quantum gates on the IBM quantum processor

The experimental implementation of selective quantum process tomography (SQPT) involves computing individual elements of the process matrix with the help of a special set of states called quantum 2-design states. However, the number of experimental settings required to prepare input states from quantum 2-design states to selectively and precisely compute a desired element of the process matrix is still high, and hence constructing the corresponding unitary operations in the lab is a daunting task. In order to reduce the experimental complexity, we mathematically reformulated the standard SQPT problem, which we term the modified SQPT (MSQPT) method. We designed the generalized quantum circuit to prepare the required set of input states and formulated an efficient measurement strategy aimed at minimizing the experimental cost of SQPT. We experimentally demonstrated the MSQPT protocol on the IBM QX2 cloud quantum processor and selectively characterized various two- and three-qubit quantum gates.

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arXiv2020

True experimental reconstruction of quantum states and processes via convex optimization

We use a constrained convex optimization (CCO) method to experimentally characterize arbitrary quantum states and unknown quantum processes on a two-qubit NMR quantum information processor. Standard protocols for quantum state and quantum process tomography are based on linear inversion, which often result in an unphysical density matrix and hence an invalid process matrix. The CCO method on the other hand, produces physically valid density matrices and process matrices, with significantly improved fidelity as compared to the standard methods. The constrainedoptimization problem is solved with the help of a semi-definite programming (SDP) protocol. We use the CCO method to estimate the Kraus operators and characterize gates in the presence of errors due to decoherence. We then assume Markovian system dynamics and use a Lindblad master equation in conjunction with the CCO method to completely characterize the noise processes present in the NMR qubits.

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arXiv2018

Experimental demonstration of selective quantum process tomography on an NMR quantum information processor

We present the first NMR implementation of a scheme for selective and efficient quantum process tomography without ancilla. We generalize this scheme such that it can be implemented efficiently using only a set of measurements involving product operators. The method allows us to estimate any element of the quantum process matrix to a desired precision, provided a set of quantum states can be prepared efficiently. Our modified technique requires fewer experimental resources as compared to the standard implementation of selective and efficient quantum process tomography, as it exploits the special nature of NMR measurements to allow us to compute specific elements of the process matrix by a restrictive set of sub-system measurements.To demonstrate the efficacy of our scheme, we experimentally tomograph the processes corresponding to `no operation', a controlled-NOT (CNOT), and a controlled-Hadamard gate on a two-qubit NMR quantum information processor, with high fidelities.

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